As means for obtaining high hardness rubber in the past, the general practice is to blend a large amount of a crosslinking agent into a rubber. However, a crosslinking agent is generally low in solubility with a low polarity rubber such as a general purpose rubber, and therefore, if a rubber containing a large amount of a crosslinking agent is allowed to stand for a certain time or more, there was the problem that the crosslinking agent would cause blooming (or precipitating) on the rubber surface. As a method to solve such a problem, it is possible to use an insoluble sulfur, when crosslinking rubber with sulfur, so as to suppress blooming to a certain extent, but there has been no such method of solution, as in the case of using an in insoluble sulfur, in the case of rubber crosslinked with a non-sulfur type crosslinking agent such as a peroxide. However, in the case of a rubber for using in applications requiring thermal resistance (e.g., EPDM), peroxide cross-linking results in superior thermal resistance etc. compared with sulfur cross-linking and therefore is more preferable, but there has been a problem that the rubber obtained by a peroxide crosslinking is generally lower in modulus and other physical properties compared with rubber obtained by a conventional sulfur crosslinking (See, for example, Japanese Unexamined Patent Publication (Kokai) No. 6-191805).
On the other hand, a run flat tire capable of running on for a certain distance, even if the tire pressure rapidly drops due to a puncture, burst, etc. is known in the art. For example, a pneumatic tire having a run flat property using a rubber composition comprising a hydrogenated nitrile rubber containing zinc methacrylate etc. for a side reinforcing rubber layer having a crescent sectional shape has been proposed (see Japanese Unexamined Patent Publication (Kokai) No. 11-100463). This rubber composition exhibits a high hardness suitable for the side reinforcing layer of a run flat tire, but there was a problem that the vulcanization bondability with a conventional rubber used for tires is not sufficient, an adhesive rubber layer is needed, and, therefore, the productivity is poor. If the amount of the rubber composition comprising the hydrogenated nitrile rubber containing zinc methacrylate etc. is decreased, the vulcanization bondability is improved, but there is a problem that the desired strength required for a side reinforcing rubber is not able to be obtained.